Search: id:A003983
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%I A003983
%S A003983 1,1,1,1,2,1,1,2,2,1,1,2,3,2,1,1,2,3,3,2,1,1,2,3,4,3,2,1,1,2,3,4,4,3,2,
%T A003983 1,1,2,3,4,5,4,3,2,1,1,2,3,4,5,5,4,3,2,1,1,2,3,4,5,6,5,4,3,2,1,1,2,3,4,
%U A003983 5,6,6,5,4,3,2,1,1,2,3,4,5,6,7,6,5,4,3,2,1,1,2,3,4,5,6,7,7,6,5,4,3,2,1
%N A003983 Array read by antidiagonals with T(n,k) = min(n,k).
%C A003983 Also, "correlation triangle" for the constant sequence 1. - Paul Barry 
               (pbarry(AT)wit.ie), Jan 16 2006
%C A003983 Antidiagonal sums are in A002620.
%C A003983 As a triangle, row sums are A002620. T(2n,n)=n+1. Diagonal sums are A001399. 
               Construction: Take antidiagonal triangle of MM^T where M is the sequence 
               array for the constant sequence 1 (lower triangular matrix with all 
               1's). - Paul Barry (pbarry(AT)wit.ie), Jan 16 2006
%F A003983 Number triangle T(n, k)=sum{j=0..n, [j<=k][j<=n-k]}. - Paul Barry (pbarry(AT)wit.ie), 
               Jan 16 2006
%F A003983 G.f.: 1/((1-x)*(1-x*y)*(1-x^2*y)) (Christian G. Bower (bowerc(AT)usa.net), 
               Jan 17 2006)
%e A003983 Triangle version begins
%e A003983 1,
%e A003983 1, 1,
%e A003983 1, 2, 1,
%e A003983 1, 2, 2, 1,
%e A003983 1, 2, 3, 2, 1,
%e A003983 1, 2, 3, 3, 2, 1,
%e A003983 1, 2, 3, 4, 3, 2, 1,
%e A003983 1, 2, 3, 4, 4, 3, 2, 1,
%e A003983 1, 2, 3, 4, 5, 4, 3, 2, 1
%Y A003983 Cf. A002620, A001399, A087062, A115236, A115237, A124258.
%Y A003983 Sequence in context: A156593 A054526 A113453 this_sequence A087062 A110537 
               A144434
%Y A003983 Adjacent sequences: A003980 A003981 A003982 this_sequence A003984 A003985 
               A003986
%K A003983 tabl,nonn,easy,nice
%O A003983 1,5
%A A003983 Marc LeBrun (mlb(AT)well.com)
%E A003983 More terms from Larry Reeves (larryr(AT)acm.org), Nov 08 2000
%E A003983 Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Dec 05 2006

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